Continuous Attractor Models Research Articles

The time course and organization of hippocampal replay.

The mechanisms by which the brain replays neural activity sequences remain unknown. Recording from large ensembles of hippocampal place cells in freely behaving rats, we observed that replay content is strictly organized over multiple timescales and governed by self-avoidance. After movement cessation, replays avoided the animal's previous path for 3 seconds. Chains of replays avoided self-repetition over a shorter timescale. We used a continuous attractor model of neural activity to demonstrate that neuronal fatigue both generates replay sequences and produces self-avoidance over the observed timescales. In addition, replay of past experience became predominant later into the stopping period, in a manner requiring cortical input. These results indicate a mechanism for replay generation that unexpectedly constrains which sequences can be produced across time.

A Continuous Attractor Model with Realistic Neural and Synaptic Properties Quantitatively Reproduces Grid Cell Physiology.

Computational simulations with data-driven physiological detail can foster a deeper understanding of the neural mechanisms involved in cognition. Here, we utilize the wealth of cellular properties from Hippocampome.org to study neural mechanisms of spatial coding with a spiking continuous attractor network model of medial entorhinal cortex circuit activity. The primary goal is to investigate if adding such realistic constraints could produce firing patterns similar to those measured in real neurons. Biological characteristics included in the work are excitability, connectivity, and synaptic signaling of neuron types defined primarily by their axonal and dendritic morphologies. We investigate the spiking dynamics in specific neuron types and the synaptic activities between groups of neurons. Modeling the rodent hippocampal formation keeps the simulations to a computationally reasonable scale while also anchoring the parameters and results to experimental measurements. Our model generates grid cell activity that well matches the spacing, size, and firing rates of grid fields recorded in live behaving animals from both published datasets and new experiments performed for this study. Our simulations also recreate different scales of those properties, e.g., small and large, as found along the dorsoventral axis of the medial entorhinal cortex. Computational exploration of neuronal and synaptic model parameters reveals that a broad range of neural properties produce grid fields in the simulation. These results demonstrate that the continuous attractor network model of grid cells is compatible with a spiking neural network implementation sourcing data-driven biophysical and anatomical parameters from Hippocampome.org. The software (version 1.0) is released as open source to enable broad community reuse and encourage novel applications.

Cholinergic Neuromodulation of Prefrontal Attractor Dynamics Controls Performance in Spatial Working Memory.

The behavioral and neural effects of the endogenous release of acetylcholine following stimulation of the nucleus basalis (NB) of Meynert have been recently examined in two male monkeys (Qi et al., 2021). Counterintuitively, NB stimulation enhanced behavioral performance while broadening neural tuning in the prefrontal cortex (PFC). The mechanism by which a weaker mnemonic neural code could lead to better performance remains unclear. Here, we show that increased neural excitability in a simple continuous bump attractor model can induce broader neural tuning and decrease bump diffusion, provided neural rates are saturated. Increased memory precision in the model overrides memory accuracy, improving overall task performance. Moreover, we show that bump attractor dynamics can account for the nonuniform impact of neuromodulation on distractibility, depending on distractor distance from the target. Finally, we delve into the conditions under which bump attractor tuning and diffusion balance in biologically plausible heterogeneous network models. In these discrete bump attractor networks, we show that reducing spatial correlations or enhancing excitatory transmission can improve memory precision. Altogether, we provide a mechanistic understanding of how cholinergic neuromodulation controls spatial working memory through perturbed attractor dynamics in the PFC.

Place cells dynamically refine grid cell activities to reduce error accumulation during path integration in a continuous attractor model

Navigation is one of the most fundamental skills of animals. During spatial navigation, grid cells in the medial entorhinal cortex process speed and direction of the animal to map the environment. Hippocampal place cells, in turn, encode place using sensory signals and reduce the accumulated error of grid cells for path integration. Although both cell types are part of the path integration system, the dynamic relationship between place and grid cells and the error reduction mechanism is yet to be understood. We implemented a realistic model of grid cells based on a continuous attractor model. The grid cell model was coupled to a place cell model to address their dynamic relationship during a simulated animal’s exploration of a square arena. The grid cell model processed the animal’s velocity and place field information from place cells. Place cells incorporated salient visual features and proximity information with input from grid cells to define their place fields. Grid cells had similar spatial phases but a diversity of spacings and orientations. To determine the role of place cells in error reduction for path integration, the animal’s position estimates were decoded from grid cell activities with and without the place field input. We found that the accumulated error was reduced as place fields emerged during the exploration. Place fields closer to the animal’s current location contributed more to the error reduction than remote place fields. Place cells’ fields encoding space could function as spatial anchoring signals for precise path integration by grid cells.

A Spiking Neural Network Model of Rodent Head Direction Calibrated With Landmark Free Learning.

Maintaining a stable estimate of head direction requires both self-motion (idiothetic) information and environmental (allothetic) anchoring. In unfamiliar or dark environments idiothetic drive can maintain a rough estimate of heading but is subject to inaccuracy, visual information is required to stabilize the head direction estimate. When learning to associate visual scenes with head angle, animals do not have access to the ‘ground truth' of their head direction, and must use egocentrically derived imprecise head direction estimates. We use both discriminative and generative methods of visual processing to learn these associations without extracting explicit landmarks from a natural visual scene, finding all are sufficiently capable at providing a corrective signal. Further, we present a spiking continuous attractor model of head direction (SNN), which when driven by idiothetic input is subject to drift. We show that head direction predictions made by the chosen model-free visual learning algorithms can correct for drift, even when trained on a small training set of estimated head angles self-generated by the SNN. We validate this model against experimental work by reproducing cue rotation experiments which demonstrate visual control of the head direction signal.

Neurodegenerative damage reduces firing coherence in a continuous attractor model of grid cells.

Grid cells in the dorsolateral band of the medial entorhinal cortex (dMEC) display strikingly regular periodic firing patterns on a lattice of positions in two-dimensional (2D) space. This helps animals to encode relative spatial location without reference to external cues. The dMEC is damaged in the early stages of Alzheimer's disease, which affects navigation ability of a disease victim, reducing the synaptic density of neurons in the network. Within an established two-dimensional continuous attractor neural network model of grid cell activity, we introduce neural sheet damage parametrized by radius and by the strength of the synaptic output for neurons in the damaged region. The mean proportionality of the grid field flow rate in the dMEC to the velocity of the model animal is maintained, but there is a broadened distribution of flow rates in the damaged case. This flow-rate-to-velocity proportionality is essential to establish coherent grid firing fields for individual grid cells for a roaming animal. When we examine the coherence of the grid cell firing field by studying Bragg peaks of the Fourier transformed lattice firing field intensity in both damaged and undamaged regions, we find that, for a wide range of damage radius and reduced synaptic strength, for undamaged model grid cells there is an incoherent firing field structure with only a single central peak. In the radius-damage plane this is adjacent to narrow bands of striped lattices (two additional Bragg peaks), which abut an orthorhombic pattern (four additional Bragg peaks), that abuts the undamaged hexagonal region (six additional Bragg peaks). Within the damaged region, grid cells show no Bragg peaks outside the central one, which shows reduced intensity with increasing damage, and outside the damaged region the central Bragg peak strength is largely unaffected. There is a reentrant region of normal grid firing fields for very large damage area. We anticipate that the modified grid cell behavior can be observed in noninvasive functional magnetic resonance imaging (fMRI) of the dMEC.

Grid cells are modulated by local head direction

Grid and head direction codes represent cognitive spaces for navigation and memory. Pure grid cells generate grid codes that have been assumed to be independent of head direction, whereas conjunctive cells generate grid representations that are tuned to a single head direction. Here, we demonstrate that pure grid cells also encode head direction, but through distinct mechanisms. We show that individual firing fields of pure grid cells are tuned to multiple head directions, with the preferred sets of directions differing between fields. This local directional modulation is not predicted by previous continuous attractor or oscillatory interference models of grid firing but is accounted for by models in which pure grid cells integrate inputs from co-aligned conjunctive cells with firing rates that differ between their fields. We suggest that local directional signals from grid cells may contribute to downstream computations by decorrelating different points of view from the same location.

Stability of working memory in continuous attractor networks under the control of short-term plasticity.

Continuous attractor models of working-memory store continuous-valued information in continuous state-spaces, but are sensitive to noise processes that degrade memory retention. Short-term synaptic plasticity of recurrent synapses has previously been shown to affect continuous attractor systems: short-term facilitation can stabilize memory retention, while short-term depression possibly increases continuous attractor volatility. Here, we present a comprehensive description of the combined effect of both short-term facilitation and depression on noise-induced memory degradation in one-dimensional continuous attractor models. Our theoretical description, applicable to rate models as well as spiking networks close to a stationary state, accurately describes the slow dynamics of stored memory positions as a combination of two processes: (i) diffusion due to variability caused by spikes; and (ii) drift due to random connectivity and neuronal heterogeneity. We find that facilitation decreases both diffusion and directed drifts, while short-term depression tends to increase both. Using mutual information, we evaluate the combined impact of short-term facilitation and depression on the ability of networks to retain stable working memory. Finally, our theory predicts the sensitivity of continuous working memory to distractor inputs and provides conditions for stability of memory.

A Map-like Micro-Organization of Grid Cells in the Medial Entorhinal Cortex

How the topography of neural circuits relates to their function remains unclear. Although topographic maps exist for sensory and motor variables, they are rarely observed for cognitive variables. Using calcium imaging during virtual navigation, we investigated the relationship between the anatomical organization and functional properties of grid cells, which represent a cognitive code for location during navigation. We found a substantial degree of grid cell micro-organization in mouse medial entorhinal cortex: grid cells and modules all clustered anatomically. Within a module, the layout of grid cells was a noisy two-dimensional lattice in which the anatomical distribution of grid cells largely matched their spatial tuning phases. This micro-arrangement of phases demonstrates the existence of a topographical map encoding a cognitive variable in rodents. It contributes to a foundation for evaluating circuit models of the grid cell network and is consistent with continuous attractor models as the mechanism of grid formation.

Multiple Choice Neurodynamical Model of the Uncertain Option Task.

The uncertain option task has been recently adopted to investigate the neural systems underlying the decision confidence. Latterly single neurons activity has been recorded in lateral intraparietal cortex of monkeys performing an uncertain option task, where the subject is allowed to opt for a small but sure reward instead of making a risky perceptual decision. We propose a multiple choice model implemented in a discrete attractors network. This model is able to reproduce both behavioral and neurophysiological experimental data and therefore provides support to the numerous perspectives that interpret the uncertain option task as a sensory-motor association. The model explains the behavioral and neural data recorded in monkeys as the result of the multistable attractor landscape and produces several testable predictions. One of these predictions may help distinguish our model from a recently proposed continuous attractor model.

Hebbian Plasticity Realigns Grid Cell Activity with External Sensory Cues in Continuous Attractor Models.

After the discovery of grid cells, which are an essential component to understand how the mammalian brain encodes spatial information, three main classes of computational models were proposed in order to explain their working principles. Amongst them, the one based on continuous attractor networks (CAN), is promising in terms of biological plausibility and suitable for robotic applications. However, in its current formulation, it is unable to reproduce important electrophysiological findings and cannot be used to perform path integration for long periods of time. In fact, in absence of an appropriate resetting mechanism, the accumulation of errors over time due to the noise intrinsic in velocity estimation and neural computation prevents CAN models to reproduce stable spatial grid patterns. In this paper, we propose an extension of the CAN model using Hebbian plasticity to anchor grid cell activity to environmental landmarks. To validate our approach we used as input to the neural simulations both artificial data and real data recorded from a robotic setup. The additional neural mechanism can not only anchor grid patterns to external sensory cues but also recall grid patterns generated in previously explored environments. These results might be instrumental for next generation bio-inspired robotic navigation algorithms that take advantage of neural computation in order to cope with complex and dynamic environments.

Sensory feedback in a bump attractor model of path integration.

Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.

A Hybrid Oscillatory Interference/Continuous Attractor Network Model of Grid Cell Firing

Grid cells in the rodent medial entorhinal cortex exhibit remarkably regular spatial firing patterns that tessellate all environments visited by the animal. Two theoretical mechanisms that could generate this spatially periodic activity pattern have been proposed: oscillatory interference and continuous attractor dynamics. Although a variety of evidence has been cited in support of each, some aspects of the two mechanisms are complementary, suggesting that a combined model may best account for experimental data. The oscillatory interference model proposes that the grid pattern is formed from linear interference patterns or "periodic bands" in which velocity-controlled oscillators integrate self-motion to code displacement along preferred directions. However, it also allows the use of symmetric recurrent connectivity between grid cells to provide relative stability and continuous attractor dynamics. Here, we present simulations of this type of hybrid model, demonstrate that it generates intracellular membrane potential profiles that closely match those observed in vivo, addresses several criticisms aimed at pure oscillatory interference and continuous attractor models, and provides testable predictions for future empirical studies.

Impact of noise on theta-nested gamma oscillations in a spiking continuous attractor model of grid cells

Grid cells in the medial entorhinal cortex (MEC) encode location through firing fields that form grid-like maps of the environment. At the same time network activity in the MEC is dominated by oscillations in the theta (4-12 Hz) and gamma (30-100 Hz) bands. Our recent experimental data established that feedback inhibition between excitatory stellate cells and inhibitory fast spiking interneurons dominates the synaptic connectivity in layer II of the MEC, and that continuous attractor models derived from these properties are sufficient to explain both the network oscillations and grid firing fields [1]. Here we use a spiking continuous attractor network model of layer II stellate cells and fast spiking interneurons to examine the effect of intrinsic noise on the emergence of theta nested-gamma oscillations. In this model, stellate cells connect exclusively to interneurons, while interneurons contact only stellate cells. When driven with a theta (8 Hz) modulated external input, we observed network synchronization in the gamma range during the trough of the theta signal, which depended on the amount of intrinsic Gaussian noise generated independently at each neuron. Without noise, the network exhibited aberrant hyper-synchronous firing of a subpopulation of stellate cells at the beginning of each theta cycle. The stellate cell firing resulted in a strong feedback inhibitory postsynaptic currents from fast spiking interneurons that had an additional synchronizing effect. The strong inhibitory feedback abolished nested gamma oscillations. With increasing noise, the network entered an intermediate state in which we observed theta nested-gamma oscillations [1]. When noise level was set even higher, the nested gamma oscillations disappeared without increasing the amount of inhibitory coupling. We also present the impact of noise on bump attractor formation and gridness score of the grid-like receptive fields. Together, these results show that the presence of noise may have profound implications on the stability of theta-nested gamma oscillations in attractor neural circuits with feedback inhibition.

Circuits supporting the grid

Two studies show that local inhibitory connectivity and hippocampal excitatory input support the spatial firing patterns of entorhinal grid cells, providing support for continuous attractor model of grid cell firing.

The emergence of entorhinal grids is reconsidered: ARMA models with multimodal integration may explain the hippocampal formation

Event Abstract Back to Event The emergence of entorhinal grids is reconsidered: ARMA models with multimodal integration may explain the hippocampal formation Gabor Szirtes1* and András Lorincz1 1 Eötvös Loránd University, Faculty of Informatics, Hungary We refine our autoregressive moving average (ARMA) model [A. Lőrincz and G. Szirtes, Here and now: how time segments may become events in the hippocampus, Neural Networks 22:738-747,2009] of the hippocampal formation (HF) which considers model identification of sensory signals as the central role of HF. We argue that this single principle and the constraint of Hebbian learning can explain the complex, loopy connection system as well as the surprising spatial discharge patterns of the place and grid cells even without explicitly considering space related (e.g. self-motion) information. Thus we explain the discharge patterns by statistics driven learning processes instead of resorting to either intrinsic single cell dynamics (interference models) or network dynamics (continuous attractor models). Our proposed model, however, may be slow or unresponsive when observed signals do not follow the learnt statistics due to noise or changes in the underlying dynamical systems (e.g. caused by moving from one environment into another one). For this reason we endow our system with a learning module that can integrate information of different sources and can maintain or correct the activity of grid units (needed to provide a robust metric for spatial navigation) even if 1, sensory inputs are not yet appropriately registered (preserving the grids in a novel maze) or 2, inputs are not reliable (temporary maintenance of grids without visual cues). In contrast to other models on grid formation, our extended ARMA model can explain the observed parametric distortion of the grid fields, too. Conference: IBRO International Workshop 2010, Pécs, Hungary, 21 Jan - 23 Jan, 2010. Presentation Type: Poster Presentation Topic: Cognition and behavior Citation: Szirtes G and Lorincz A (2010). The emergence of entorhinal grids is reconsidered: ARMA models with multimodal integration may explain the hippocampal formation. Front. Neurosci. Conference Abstract: IBRO International Workshop 2010. doi: 10.3389/conf.fnins.2010.10.00186 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 02 May 2010; Published Online: 02 May 2010. * Correspondence: Gabor Szirtes, Eötvös Loránd University, Faculty of Informatics, Budapest, Hungary, gabor_szirtes@yahoo.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Gabor Szirtes András Lorincz Google Gabor Szirtes András Lorincz Google Scholar Gabor Szirtes András Lorincz PubMed Gabor Szirtes András Lorincz Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Evaluation of the Oscillatory Interference Model of Grid Cell Firing through Analysis and Measured Period Variance of Some Biological Oscillators

Models of the hexagonally arrayed spatial activity pattern of grid cell firing in the literature generally fall into two main categories: continuous attractor models or oscillatory interference models. Burak and Fiete (2009, PLoS Comput Biol) recently examined noise in two continuous attractor models, but did not consider oscillatory interference models in detail. Here we analyze an oscillatory interference model to examine the effects of noise on its stability and spatial firing properties. We show analytically that the square of the drift in encoded position due to noise is proportional to time and inversely proportional to the number of oscillators. We also show there is a relatively fixed breakdown point, independent of many parameters of the model, past which noise overwhelms the spatial signal. Based on this result, we show that a pair of oscillators are expected to maintain a stable grid for approximately t = 5µ 3 /(4πσ) 2 seconds where µ is the mean period of an oscillator in seconds and σ2 its variance in seconds2. We apply this criterion to recordings of individual persistent spiking neurons in postsubiculum (dorsal presubiculum) and layers III and V of entorhinal cortex, to subthreshold membrane potential oscillation recordings in layer II stellate cells of medial entorhinal cortex and to values from the literature regarding medial septum theta bursting cells. All oscillators examined have expected stability times far below those seen in experimental recordings of grid cells, suggesting the examined biological oscillators are unfit as a substrate for current implementations of oscillatory interference models. However, oscillatory interference models can tolerate small amounts of noise, suggesting the utility of circuit level effects which might reduce oscillator variability. Further implications for grid cell models are discussed.

Accurate Path Integration in Continuous Attractor Network Models of Grid Cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

Similarity Effect and Optimal Control of Multiple-Choice Decision Making

Decision making with several choice options is central to cognition. To elucidate the neural mechanisms of such decisions, we investigated a recurrent cortical circuit model in which fluctuating spiking neural dynamics underlie trial-by-trial stochastic decisions. The model encodes a continuous analog stimulus feature and is thus applicable to multiple-choice decisions. Importantly, the continuous network captures similarity between alternatives and possible overlaps in their neural representation. Model simulations accounted for behavioral as well as single-unit neurophysiological data from a recent monkey experiment and revealed testable predictions about the patterns of error rate as a function of the similarity between the correct and actual choices. We also found that the similarity and number of options affect speed and accuracy of responses. A mechanism is proposed for flexible control of speed-accuracy tradeoff, based on a simple top-down signal to the decision circuit that may vary nonmonotonically with the number of choice alternatives.

Cannabinoid-Mediated Disinhibition and Working Memory: Dynamical Interplay of Multiple Feedback Mechanisms in a Continuous Attractor Model of Prefrontal Cortex

Recurrent excitation is believed to underlie persistent neural activity observed in the prefrontal cortex and elsewhere during working memory. However, other positive and negative feedback mechanisms, operating on disparate timescales, may also play significant roles in determining the behavior of a working memory circuit. In this study, we examined dynamical interactions of multiple feedback mechanisms in a biophysically based neural model of spatial working memory. In such continuous attractor networks, a self-sustained activity pattern tends to drift randomly, resulting in a decreased accuracy of memory over time. Moreover, attractor states become unstable when spike-frequency adaptation reduces the excitability of persistently firing pyramidal neurons. Here, we show that a slow activity-dependent local disinhibition, namely cannabinoid-dependent depolarization-induced suppression of inhibition (DSI), can counteract these destabilizing effects, rendering working memory function more robust. In addition, the slow DSI effect gives rise to trial-to-trial correlations of memory-guided behavioral responses. On the other hand, computer simulations revealed that a global cannabinoid agonist (mimicking the effect of drug intake) yields the opposite effect. Thus, this work suggests a circuit scenario according to which endogenous DSI is beneficial for, whereas an exogenous drug such as marijuana is detrimental to, working memory and possibly other prefrontal functions.